Question

Math ...

Answer 1

@jim_thompson5910

Answer 2

I mainly need help with the last question about how the slope of the line can be determined from its parametric equations

Answer 3

when t = -1, what is the value of x?

Answer 4

Can you give me a moment please? I will be back in a couple of seconds

Answer 5

ok

Answer 6

I am back

Answer 7

tell me what you get

Answer 8

x = -1

Answer 9

incorrect

Answer 10

I am sorry I did 1 instead of -1

Answer 11

x = -4 + 3t

x = -4 + 3(-1)

x = -4 - 3

x = ????

Answer 12

But x = -7 ?

Answer 13

yes

Answer 14

when t = -1, y = ????

Answer 15

y = -1

Answer 16

yes so we know that (-7, -1) is one point on this line

Answer 17

when t = 0, what is the value of (x,y) ?

Answer 18

x = -4
y = 1

Answer 19

so (-4,1) is another point on this line

Answer 20

when t = 2, what is the value of (x,y) ?

Answer 21

x = 2

Answer 22

y = ??

Answer 23

y = 5

Answer 24

yes

Answer 25

so (2,5) is that third point

Answer 26

to prove it's collinear, you need to show that the slope is the same no matter which 2 points you pick

use the slope formula
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 27

Since the slope from one point to the other is the same from Point A to B and Point B to C, we can prove that it's collinear. Slope = 2/3

Answer 28

ie, let
point A = (-7,-1)
point B = (-4,1)
point C = (2,5)

you need to show that

slope of line segment AB = slope of line segment BC = slope of line segment AC

Answer 29

Line segment AB = 2/3
Line segment BC = 4/6
Line segment AC = 6/9

Answer 30

These are all of the slopes

Answer 31

they all reduce to 2/3, so yes, the points are collinear

Answer 32

What about the question for how I should derive the slope from its parametric equations?

Answer 33

You would just explain to the teacher that you found the points that correspond to the given t values. Then you use the slope formula

Answer 34

Oh okay! Thanks again :)

Answer 35

no problem

Answer 36

A couple more? Please

Answer 37

It's Exeter math and it's geometry on top of that :(

Answer 38

ok go ahead

Answer 39

Thank you SSOOOOOO SOOOO much!

Answer 40

sure thing